Computer Science > Distributed, Parallel, and Cluster Computing

Title:Distributed Recoloring

Abstract: Given two colorings of a graph, we consider the following problem: can we
recolor the graph from one coloring to the other through a series of elementary
changes, such that the graph is properly colored after each step?
We introduce the notion of distributed recoloring: The input graph represents
a network of computers that needs to be recolored. Initially, each node is
aware of its own input color and target color. The nodes can exchange messages
with each other, and eventually each node has to stop and output its own
recoloring schedule, indicating when and how the node changes its color. The
recoloring schedules have to be globally consistent so that the graph remains
properly colored at each point, and we require that adjacent nodes do not
change their colors simultaneously.
We are interested in the following questions: How many communication rounds
are needed (in the LOCAL model of distributed computing) to find a recoloring
schedule? What is the length of the recoloring schedule? And how does the
picture change if we can use extra colors to make recoloring easier?
The main contributions of this work are related to distributed recoloring
with one extra color in the following graph classes: trees, $3$-regular graphs,
and toroidal grids.